That's along the NJT Raritan Valley Line.
You can take it to Newark Penn Station and then catch the PATH to Jersey City (you'll have to make another transfer at Grove Street if you work at Pavonia/Newport)
Here's the schedule:
http://www.njtransit.com/pdf/rail/R0060.pdf
The closest station to you is Annandale, but you don't have a whole lot of options for trains there. If you drive to Raritan, you have more options.
The fare is $291 per month from Raritan or $308 from Annandale. The PATH fare is $65 per month (technically, you can avoid this by taking the #1 bus from Newark to Jersey City for free because you have the rail pass, but it probably takes too long to be worth it).
There are a few North Jersey Coast Line trains that run into Hoboken, and your rail pass would be valid on them:
http://www.njtransit.com/pdf/rail/R0080.pdf
From Hoboken, you can catch the Hudson-Bergen Light Rail into Jersey City.
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